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On the exterior problem for parabolic k-Hessian equations
On the optimal decay rate of the weakly damped wave equation
Politecnico di Milano - Dipartimento di Matematica, Via Bonardi 9, 20133 Milano, Italy |
We provide a proof via direct energy estimates of the optimal exponential decay rate of the semigroup generated by the weakly damped wave equation.
References:
| [1] |
M. Conti, L. Liverani and V. Pata,
The MGT-Fourier model in the supercritical case, J. Differ. Equ., 301 (2021), 543-567.
|
| [2] |
F. Dell'Oro and V. Pata,
Second order linear evolution equations with general dissipation, Appl. Math. Optim., 83 (2021), 1877-1917.
|
| [3] |
K. J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Springer-Verlag, New York, 2000. |
| [4] |
G. R. Goldstein, J. A. Goldstein and G. Perla Menzala,
On the overdamping phenomenon: a general result and applications, Quart. Appl. Math., 71 (2013), 183-199.
|
| [5] |
G. R. Goldstein, J. A. Goldstein and G. Reyes,
Overdamping and energy decay for abstract wave equations with strong damping, Asymptot. Anal., 88 (2014), 217-232.
|
| [6] |
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983. |
show all references
References:
| [1] |
M. Conti, L. Liverani and V. Pata,
The MGT-Fourier model in the supercritical case, J. Differ. Equ., 301 (2021), 543-567.
|
| [2] |
F. Dell'Oro and V. Pata,
Second order linear evolution equations with general dissipation, Appl. Math. Optim., 83 (2021), 1877-1917.
|
| [3] |
K. J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Springer-Verlag, New York, 2000. |
| [4] |
G. R. Goldstein, J. A. Goldstein and G. Perla Menzala,
On the overdamping phenomenon: a general result and applications, Quart. Appl. Math., 71 (2013), 183-199.
|
| [5] |
G. R. Goldstein, J. A. Goldstein and G. Reyes,
Overdamping and energy decay for abstract wave equations with strong damping, Asymptot. Anal., 88 (2014), 217-232.
|
| [6] |
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983. |
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